We present a quasiperiodic self-dual metric of the Gibbons{Hawking type with one gravitational instanton per spacetime cell. The solution, based on an adaptation of Weierstrassian and functions to three dimensions, conforms to a de nition of spacetime foam given by Hawking. Permanent addresss: Physics Department, Bo~gazi ci University, 80815 Bebek{_ Istanbul, Turkey

We prove the theorem: The necessary and sufficient condition for a spherically symmetric spacetime to represent an isothermal perfect fluid (barotropic equation of state with density falling off as inverse square of the curvature radius) distribution without boundary is that it is conformal to the “minimally” curved (gravitation only manifesting in tidal acceleration and being absent in particl...

We study the propagation of electromagnetic waves in a spacetime devoid of a metric but equipped with a linear electromagnetic spacetime relation H ∼ χ · F . Here H is the electromagnetic excitation (D,H) and F the field strength (E,B), whereas χ (36 independent components) characterizes the electromagnetic permittivity/permeability of spacetime. We derive analytically the corresponding Fresnel...

We have estimated higher order quantum gravity corrections to de Sitter spacetime. Our results suggest that, while the classical spacetime metric may be distorted by the graviton self-interactions, the corrections are relatively weaker than previously thought, possibly growing like a power rather than exponentially in time. Permanent address: ITEP, 113259, Moscow, Russia.

Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates of the observer. It is then useful to consider the tangent bundle of spacetime with spacetime in the base manifold and four-velocity space in the fiber. A ph...

We discuss a model of a conformal p-brane interacting with the world volume metric and connection. The purpose of the model is to suggest a mechanism by which gravity coupled to p-branes leads to the formation of structure rather than homogeneity in spacetime. Furthermore, we show that the formation of structure is accompanied by the appearance of a multivalued cosmological constant, i.e., one ...

A cylindrically symmetric perfect fluid spacetime with no curvature singularity is shown. The equation of state for the perfect fluid is that of a stiff fluid. The metric is diagonal and non-separable in comoving coordinates for the fluid. It is proven that the spacetime is geodesically complete and globally hyperbolic. PACS 04.20.Jb, 98.80.Hw

By extending the charged Vaidya metric to cover all of spacetime, we obtain a Penrose diagram for the formation and evaporation of a charged black hole. In this construction, the singularity is time-like. The entire spacetime can be predicted from initial conditions if boundary conditions at the singularity are known.

The problem of merging General Relativity with Quantum Field Theory is known as Quantum Gravity. One aspect of this merged theories is that at the Planck scale, spacetime could be subjected to topology and metric fluctuations[1]. Such a fluctuating spacetime is known under the name of “spacetime foam” which can be taken as a model for the quantum gravitational vacuum. At this scale of lengths (...

We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painlevé-Gullstrand form of the spacetime metric, whereas the data of the Randers problem ar...